Comparison of IDA and multicomponent IDA-based fragility analysis

Comparison of IDA and multicomponent IDA-based fragility analysis Mohsen Soltani (  M.Soltani1@stu.qom.ac.ir ) University of Qom Rouhollah Amirabadi University of Qom Mahdi Sharifi University of Qom Research Article Keywords: MIDA, IDA, Fragility curve, Fragility surface Posted Date: August 4th, 2022 DOI: https://doi.org/10.21203/rs.3.rs-1904409/v1 License:   This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Page 1/29 Abstract The results of the fragility analysis of important structures depend on the accuracy of structural analysis. Incremental dynamic analysis (IDA) and multicomponent IDA (MIDA) are commonly-used structural analysis methods for the seismic assessment of structures. The present paper aims to evaluate the seismic performance of a structure with high seismic vulnerability using IDA and MIDA-based fragility analysis. A numerical model was used to model a typical wharf. Next, Pushover analysis, IDA, and MIDA along randomly-selected incident angles were performed. The results of each analysis were converted to a response surface by extrapolation. The response surface presented the zones, which included the critical responses. The difference between the response surface of MIDA and IDA at the global instability was approximately 38%. Further, the fragility surfaces of IDA and MIDA results were developed. The critical zones presented by MIDA and IDA fragility surfaces were not identical, particularly at the serviceability limit state. There was a difference of 11% and 20% between MIDA and IDA fragility surfaces, where the responses exceeded the reparability and near collapse limit state, respectively. The results showed that implementing the developed form of IDA (MIDA) could optimize the input data of fragility analysis for structures with high seismic vulnerability. 1. Introduction Serviceability and operation of ports play a significant role in the global economy. These structures are mainly located in areas at high risk for natural hazards such as earthquakes and floods. Past earthquakes caused substantial damage and economic losses to ports. The fragility analysis was used to assess the seismic vulnerability of ports and predict the risk of disruption in port operations. Fragility analysis determined the probability of exceeding the structural response from a predefined limit state for a structure subjected to external loads (SEAOC 1995; Korkmaz 2008; Shinozuka 2000). This analysis has been used in many studies (Karim and Yamazaki 2001; Lagaros et al. 2009; Tavares et al. 2013; Muntasir Billah and Shahria Alam 2015; Wang et al. 2018; He and Lu 2018; Jeon et al. 2019; Bakhshinezhad and Mohebi 2019; Naderpour and Vakili 2019; Karimzadeh et al. 2020; Altieri and Patelli 2020; Forcellini 2021; Stefanidou et al. 2022; Zhang et al. 2022). The fragility analysis has been performed in different marine structure studies. Chiou et al. (2011) presented a step-by-step procedure of fragility analysis by Microsoft Excel software for the Kaohsiung port. Amirabadi et al. (2012) modeled seven pile-supported wharves to propose an optimized probabilistic seismic demand model (PSDM) using fragility analysis. Ragued et al. (2014) used the fragility function to investigate different liquefiable soil profiles for port structures. More recently, Xie et al. (2017) modeled a single pile in different slopes and section sizes to extract one formula based on their behaviors. The fragility analysis results demonstrated that the presented formula was well integrated into a high-piled offshore structure. Balomenos and Padgett (2018) proposed a methodology for the fragility analysis of typical wharf structures subjected to storm surges and waves. Page 2/29 Ko and Yang (2019) simulated seismic damages of the earthquake that occurred in 2018 by performing the fragility analysis for a wharf constructed in Taiwan. Su et al. (2019a) numerically modeled a pilesupported pier and measured the effect of soil permeability on the structure's seismic performance through developing fragility curves. Su et al. (2019b) performed the fragility analysis to assess common soil improvement methods for a pile-supported wharf. Johnson et al. (2019) assessed the port of San Francisco using seismic fragility analysis. Mina et al. (2020) performed the fragility analysis and assessed the seismic vulnerability of unburied subsea pipelines. Zhang et al. (2021) simulated a piled pier system installed in soft clay and used the fragility function to assess the system’s seismic performance. Maniglio et al. (2021) presented a methodology for port structures to develop parameterized fragility models. Mirzaeefard et al. (2021) implemented the timedependent fragility analysis for the Los Angles port. Mirzaeefard et al. (2021) used an aging-dependent seismic fragility function and performed the life-cycle cost analysis for pile-supported wharves. Huang et al. (2022) implemented fragility analysis for a coastal bridge exposed to the wave load and assessed the role of different connections in reducing the failure probability of bridges. Guetaffi et al. (2022) conducted the fragility analysis for a soil-pile structure. Rajkumari et al. (2022) reviewed studies performed by the fragility analysis. Some studies used a fragility surface to assess different structures (Seyedi et al. 2010; Petrone et al. 2020; He et al. 2020; Karafagka et al. 2021; Li et al. 2021; Shao et al. 2021). In recent studies for marine structures, Liang et al. (2020) developed seismic fragility surfaces for offshore bridges to evaluate the corrosion impacts. Soltani and Amirabadi (2021) developed the IDA-based fragility surface for a typical wharf. The reliability of input data used for the fragility analysis depends on the accuracy of structural analysis. The IDA method is a typical structural analysis compatible with the fragility analysis (Vamvatsikos and Cornell 2002). This method has been frequently used in many fragility studies. Bakhshinezhad and Mohebbi (2019) developed IDA-based fragility curves to investigate structures equipped with dampers when existing uncertainties in the input excitation, structure, and control device parameters were considered. They concluded that the effect of input excitation on the seismic responses was more critical than the other parameters. Naderpour and Vakili (2019) investigated the impact of earthquake sequences using IDA-based fragility curves. The results showed that this phenomenon had a severe effect on seismic responses. Han and Chopra (2006) considered several buildings different in stories and performed IDA and modal pushover analysis (MPA). Compared to the IDA method, the MPA procedure presented satisfactory responses for different limit states. Page 3/29 Fanaie and Ezzatshoar (2014) performed the IDA method to develop fragility curves for concentric bracing systems used for several buildings of different stories. Brunesi et al. (2015) evaluated progressive collapse risk assessment for a low-rise concrete frame structure by developing IDA-based fragility curves. Wang et al. (2015) evaluated the crack propagation within a dam through the IDA method. Cavalagli et al. (2017) performed IDA for a masonry bell tower to estimate the local reduction in stiffness caused by expected damage conditions. Pang et al. (2018) used the IDA method to develop seismic fragility curves for rockfill dams. IDA studies have not been limited to land structures. Assareh and Asgarian (2008) evaluated a centrifuge model of a single pile as a jacket-type offshore platform by the IDA method. Heydari-Torkamani et al. (2014) conducted a sensitivity analysis using the IDA method for an idealized pile-supported wharf. Banayan-Kermani et al. (2016) evaluated the effectiveness of FRP under aging effects as a retrofitting method for pile-supported wharves. Jahanitabar et al. (2017) assessed jacket-type offshore platforms under aging effects and suggested IDA as an appropriate analytical method for the seismic assessment. Many studies have examined the seismic performance of structures exposed to simultaneous actions of two components of earthquakes (Lopez et al. 2001; MacRac and Mattheis 2000; Athanatopoulou et al. 2005; Ghersi and PaoloRossi 2005; Rigato and Medina 2007; Rupali and Jaiswal 2017). The multicomponent IDA (MIDA) method, a developed form of the IDA method, was proposed by Lagaros (2010). In this analysis, a concrete structure was exposed to two components of earthquakes. The primary purpose of performing MIDA was to provide more accurate structural responses. Cheng et al. (2014) examined an undersea tunnel under bidirectional ground motions. Hussain et al. (2020) modeled an asymmetric structure to assess the impact of bidirectional uncertainty. They showed that the inelastic results might be underestimated if bidirectional loads of ground motions were not considered. Because the results of fragility analysis are contingent on the input data obtained by the structural analysis, the present paper aims to compare IDA and MIDA responses and evaluate the sensitivity of fragility estimation to the applied methods. A Finite element (FE) model was used to model a wharf constructed in Iran. Next, different incident angles were randomly selected as perpendicular pairs. The nonlinear pushover analysis was performed along each component of the pairs. The developed pushover curves were extrapolated to a response surface. Eleven sets of two-component time histories were selected to obtain the structural responses by MIDA and IDA methods. The fragility surface was developed based on IDA and MIDA results. 2. Structural Analysis MIDA and IDA methods are implemented by selecting the intensity measure (IM) and engineering demand parameter (EDP). IM is used to scale seismic records. There are different IMs and EDPs used in many Page 4/29 studies (Soltani and Amirabadi (2021)). Sa (T1, 5%) and pile peak responses were recommended for the fragility analysis of port structures (Amirabadi et al. 2012; PIANC 2001). The model coordinate system was defined to monitor EDP in different intensity levels along the incident angle(s) (Fig. 1). The structural axes were indicated by Ox and Oy components. Two components of each time history, called h1 and h2, were scaled and perpendicularly applied along Op and Oq directions (Fig. 1). Figure 2, as an example, displays the horizontal components of the Landers earthquake recorded in the Desert Hot Spring station. The chosen scale factors for h1 and h2 are required to provide elastic and plastic structural responses. The last phase of the MIDA and IDA method is developing response curves based on the chosen IM and EDP. According to research by Lagaros (2010), the required range of incident angles is between 0° and 180° for a symmetric structure. Therefore, the range of incident angles was considered between 0° and 180°. The increments of 5° were used to compare IDA and MIDA-based fragility analysis. 3. Model Description And Finite Element Modeling The port of Mahshahr, constructed in Iran, was considered (Fig. 3). The water level was 5.04 m below the deck (Fig. 3-a). SAP2000 software (2017) was used to model this structure. Figure 4 shows a 3D view of the model. This port was comprised of 24 vertical piles. The vertical piles were constructed with prestressed concrete (PC) and 36 pre-stressed bars. The pile wall thickness and diameter were 15 cm and 1 m, respectively (Fig. 4-c). The beam element was employed to model the vertical piles. The rigid connection was used to attach the vertical pile to the slab modeled by the shell element. Winkler springs were used to model soil-pile interactions (SPI). Material properties of Winkler springs were defined with the American Petroleum Institute’s suggestion (API) (2000). The SPT test was performed to obtain the soil properties. Fiber plastic hinges were applied along the piles to simulate the nonlinear deformations of the piles. Tables 1–2 show the material characteristics of the FE model. Table 1 Pile material characteristics Diameter (m) Bar diameter (cm) Wall thickness (cm) Effective prestress ( N ) mm 2 1 1.07 15 Page 5/29 7.4 Table 2 Soil layers’ material properties Layer No. Depth (m) Density ( kg ) cm Cohesion ( N ) cm 3 Friction angle (°) 3 Elasticity ( N ) cm 2 1 10.5 1.45 0.175 0 47.5 2 1.0 1.475 0.45 0 120 3 < 23 1.65 1.75 0 400 3.1 Validation analysis Modal and time history analyses were implemented by SAP2000 and ABAQUS (2018). Next, the results of each analysis were compared by calculation of the correlation coefficient. In the ABAQUS model, the vertical pile and deck were modeled by solid elements (Fig. 5). The tie contact was used to attach the vertical pile to the deck. The connector elements were adopted to model SPI. A temperature load was applied as the pre-stressed load to the bars of vertical piles. Table 3 shows the fundamental periods of the structure obtained by the modal analysis. The difference between the fundamental periods obtained by the FE models was insignificant. Table 3 Fundamental period obtained by SAP2000 and ABAQUS. Fundamental period Tx Ty SAP2000 1.67 1.71 ABAQUS 1.85 1.81 Eleven far-fault ground motions were obtained from the PEER database (2017) to implement the time history analysis. The far-fault criteria are i) The range of earthquakes magnitude was between 6.19 and 7.37 Mw, and ii) The range of epicentral distance was between 12 and 54 km (Chopra and Chintanapakdee (2001)) (Table 4). Eq. 7 was selected to perform the time history analysis in the SAP2000 and ABAQUS models. The time history analysis results were compared in Fig. 6. The correlation coefficient between the responses was equal to 0.9. Time history analysis has been performed for the other earthquake records. The correlation coefficients between the results are presented in Table 5. The ABAQUS and SAP2000 results were approximately equal. Because of the existing high computational loads in the ABAQUS model, using the SAP2000 model decreased the computational efforts in the structural analysis. Page 6/29 Table 4 The seismic records (PEER database 2017) No. Record Mw D (Km) PGAh1(g) PGAh2(g) Eq1 Manjil 7.37 12.55 0.359 0.496 0.72 Eq2 Landers 7.28 21.78 0.139 0.154 0.90 Eq3 Loma Prieta-1 7.1 24.32 0.247 0.239 1.03 Eq4 Loma Prieta-2 7.1 39.04 0.127 0.106 1.19 Eq5 Loma Prieta-3 7.1 54.86 0.073 0.064 1.14 Eq6 Morgan hill 6.19 45.47 0.079 0.059 1.33 Eq7 San Fernando 6.5 40 0.098 0.109 0.89 Eq8 San Fernando-2 6.61 35.54 0.091 0.123 0.73 Eq9 Northridge-1 6.69 20.11 0.544 0.373 1.45 Eq10 Northridge- 2 6.69 35.81 0.08 0.06 1.33 Eq11 Cape Mendocino 7.01 16.54 0.116 0.093 1.24 PGAh1 PGAh2 Table 5 The correlation coefficient values (cc) resulted from ABAQUS and SAP2000 model Record Eq1 Eq2 Eq3 Eq4 Eq5 Eq6 Eq7 Eq8 Eq9 Eq10 Eq11 cc 0.89 0.85 0.87 0.92 0.93 0.89 0.9 0.94 0.88 0.81 0.9 4. Implementation Of Structural Analysis Pushover analysis was performed in increments of 5°. The incident angle of earthquakes ranged between 0° and 180°. The pile peak response was recorded to develop the pushover curves through Eq. (1): 2 2 Δmax = √ΔOy + ΔOx 1 Where ∆max is the maximum value of the vector sum of the peak response, ∆oy is the pile peak response along Oy, and ∆ox is the pile peak response along Ox (Fig. 7). The response variations where the structure Page 7/29 passed the elastic zone were displayed in Fig. 7. Comparison of pushover curves revealed the similar bounds for the limit states. The development of plastic hinges in the pushover analysis was monitored to determine the bounds of limit states qualitatively suggested by PIANC (Table 6). Table 6 PIANC limit states (2000) limit states Serviceability (I) Reparability (II) Near collapse (III) The peak response of pile a pile yields at its connection to the deck The average value of the serviceability and near collapse limit states a pile reaches its ultimate capacity at the pile cap The pushover surface was developed by arranging pushover curves according to Fig. 8(a). In Fig. 8(b), the response surface contour was displayed. Because the pushover curves were similar, the response surface could provide an acceptable approximation for the structural capacity along every desired angle. It could be predicted that the zones adjacent to 45° and 135° were more susceptible to seismic loads because of having lower capacities. MIDA and IDA were used to investigate the seismic vulnerability of the zones on the response surface. The ground motions of Table 4 were adopted to develop MIDA and IDA curves. Two incident angles of 45° and 135° were initially selected as a perpendicular pair (pair (45°,135°)). For MIDA, two components of each earthquake (h1 and h2) were applied along Op and Oq. The component with the higher maximum acceleration was applied along the first component. In Eq. 11, as an example, the maximum acceleration of h1 was more than h2 (Fig. 2). The component of h1 was applied along 45° (Op direction), and h2 was applied along 135° (Oq direction). MIDA curves were developed by recording the maximum deck displacement (∆max) at each level of Sa (m/s2). Similarly, the other records were applied along Op and Oq. The earthquake component with maximum acceleration for IDA was scaled and applied along 45° and 135° separately. ∆max was obtained, and IDA curves were developed. Figure 9 presented MIDA and IDA results for 45° and 135°. The effect of the applied methods on the results was tangible. Figure 9(b) showed that MIDA responses exceeded elastic slope significantly sooner than IDA responses. The summary and surface of IDA and MIDA were developed to evaluate this effect on the other incident angles. MIDA and IDA methods were implemented for the other incident angles as above. 50% fractiles of developed IDA and MIDA curves were developed and shown in Fig. 10. Comparing the elastic slopes and global instabilities (flat lines) revealed the significant differences between the structural responses of MIDA and IDA. MIDA curve passed the elastic slope at Sa = 0.5 m/s2, while IDA response almost reached Page 8/29 the yield point at 0.6 m/s2. The displacement where the global instability for the MIDA curve occurred was larger than IDA. Because of the number of incident angles, comparing the summary curves might not be convenient. MIDA and IDA curves were converted to the response surface in the same procedure as the pushover surface. Figure 11 showed that the MIDA surface response was considerably lower than the IDA surface response. The effect of applied methods was significantly different. Compared to the MIDA surface, some critical responses, such as those close to 105° and 120°, were not considered by the IDA surface. Although the global instability (flat surface) almost occurred at Sa = 2 m/s2, there was a difference of 38% between the displacement obtained by IDA and MIDA methods. 5. Fragility Analysis Fragility analysis is mainly performed to predict damage in non-structural or structural components based on EDPs values when a selected structure is exposed to a predicted earthquake. The curve of fragility presents the probability of structural responses exceeding capacity at different levels of Sa. Generally, fragility curves are developed using a lognormal distribution function based on Eqs. (2) -(4): P [S > s|PGA] = P [X > xi |PGA] = 1 − Φ [ lnxi − λ ] ζ 2 1 λ = lnμ − ξ 2 2 3 ξ 2 2 = ln[1 + δ ] 4 φ is the function of standard normal cumulative distribution. The upper bound for the limit states is si. α and β are obtained by σ and µ. σ and µ are the standard deviations and average of data in each Sa level. The fragility curve is commonly developed through the lognormal cumulative distribution. The bounds of limit states were defined in Table 6. The lognormal cumulative distribution function was adopted to develop the fragility curves based on MIDA and IDA results. The fragility curves of MIDA and IDA are compared in each limit state and displayed in Figs. 12–14. These figures demonstrated that the IDA and MIDA fragility curves were different. In Fig. 12 (b), the exceedance probability in the serviceability limit state for all of the MIDA curves at Sa = 0.75 m/s2 was 1, while IDA curves exceeded this limit state at Sa = 0.85 m/s2. The critical incident angle of the limit states was not identical. For example, in the near collapse limit state, the critical incident angle was 120° and pair (155°,65°) for IDA and MIDA fragility Page 9/29 curves, respectively. The fragility surface was developed by extrapolating the fragility curves. Evaluation of the fragility surface makes the comparison more convenient. 5.1 Post-processing of fragility analysis The overall seismic performance of structures could be easily compared within the fragility surface. The fragility surfaces for the applied methods were developed and compared in Figs. 15 to 17. It is clear that the lower ∆θ° is considered, the more accurate the fragility surface is developed. The variation of fragility surface was significant in the serviceability limit state, and The critical incident angle was not unique in the serviceability limit state. The critical zone was determined in this limit state. In Fig. 15, as an example, the critical zone occurred between 100°-140° and 110°-135° at Sa = 0.3 m/s2 for the fragility surfaces of IDA and MIDA, respectively. The response variations decreased in fragility surfaces as the limit states changed from serviceability to near collapse limit states. This stemmed from the fact that the plastic hinges developed in the structure. However, the development of plastic hinges for MIDA occurred at lower spectral accelerations than IDA. In Fig. 16, most of the incident angles exceeded the reparability limit state at Sa = 1.125 m/s2 in the IDA fragility surface. In contrast, the MIDA-based fragility surface approximately exceeded the reparability limit state at Sa = 1 m/s2. In Fig. 17, all the angles for the IDA surface almost exceeded near collapse at 1.25 m/s2, while the fragility surface developed by the MIDA method passed this limit state at Sa = 1.18 m/s2. The difference between IDA and MIDA fragility surfaces is 11% and 20% for the reparability and near collapse limit state at P = 1. The comparison of MIDA and IDA fragility surface in the reparability and near collapse limit state revealed different critical incident angles. The critical angle was around the pair (150°,60°) and pair (115°,25°) at Sa = 0.35 m/s2 in the reparability limit state, while the critical angle for IDA was around 30° at 0.4 m/s2. The critical incident angle occurred along the pair (150°,60°) at Sa = 0.45 m/s2 and 30° at Sa = 0.55 m/s2 for MIDA and IDA fragility surface in near collapse limit state, respectively. 6. Conclusions In this paper, the results of IDA and MIDA-based fragility analysis were compared. There was a noticeable difference between the results of structural analysis obtained by the MIDA and IDA methods for a typical wharf. The comparison of MIDA and IDA results at global instability revealed that there was a difference of 38% between MIDA and IDA results. The existing difference propagated to the fragility analysis and significantly influenced the results. IDA and MIDA-based fragility surfaces were not identical in each limit state. There was also a considerable difference between the spectral accelerations where the probability reached the highest amount in each limit state. The response variation of MIDA and IDA fragility results was significant for the serviceability limit state. The difference between MIDA and IDA-based fragility surfaces was 11% and 20% when the responses exceeded the reparability and near collapse limit state, Page 10/29 respectively. The results revealed that the MIDA method could provide more optimized input data for the fragility analysis of structures with high seismic vulnerability. In addition, developing a fragility surface based on different incident angles is recommended when different scenarios of designing or retrofitting methods are investigated for important structures. Declarations Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. Competing Interests The authors have no relevant financial or non-financial interests to disclose. Author Contributions All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Mohsen Soltani, Rouhollah Amirabadi, and Mahdi Sharifi. The first draft of the manuscript was written by Mohsen Soltani, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. References 1. ABAQUS Inc (2018) Abaqus user’s manual. ABAQUS Ine, Dassault Systems, Rhode Island, USA. 2. 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Figures Figure 1 See image above for figure legend Page 16/29 Figure 2 An example of horizontal components of Landers earthquake (h1 and h2) recorded in Desert Hot Spring by PEER database (2017) Figure 3 Mahshahr port in: (a) YZ plan; (b) XY plan Page 17/29 Figure 4 FE model of Mahshahr port: (a) 3D view; (b) YZ plan; (c) pile section Page 18/29 Figure 5 ABAQUS model of Mahshahr wharf Figure 6 Time history results of SAP2000 and ABAQUS Page 19/29 Figure 7 Pushover curves in increments of 5° Figure 8 Response surface of Mahshahr port: (a) pushover curves and surface; (b) plan view of the response surface along with the limit states Page 20/29 Figure 9 (a) MIDA and IDA curves along 45° and 35° (b) Summary of MIDA and IDA curves along 45° and 135°. Page 21/29 Figure 10 50% fractiles of (a) MIDA curves (b) IDA curves Page 22/29 Figure 11 Response surface of: (a) IDA; (b) MIDA Page 23/29 Figure 12 Serviceability limit state: (a) IDA fragility curves; (b) MIDA fragility curves Page 24/29 Figure 13 Reparability limit state: (a) IDA fragility curves; (b) MIDA fragility curves Page 25/29 Figure 14 Near collapse limit state: (a) IDA fragility curves; (b) MIDA fragility curves Page 26/29 Figure 15 Serviceability: (a) IDA fragility surface; (b) MIDA fragility surface Page 27/29 Figure 16 Reparability: (a) IDA fragility surface; (b) MIDA fragility surface Page 28/29 Figure 17 Near collapse: (a) IDA fragility surface; (b) MIDA fragility surface Page 29/29